Wouldn't a decent sized centrifugal fan work for this? I thought recorders don't have all that much air resistance. In fact wikipedia mentions pipe organs use pressures in the order of 0.1 psi which equates to roughly 2.75 inch-aqua. I'm pretty sure even small centrifugal fans that were used in computers years ago can create static pressures higher than that.
The fan needs to be an impeller type and not squirrel cage. Even a ~250W furnace blower (which are squirrel cage) don't do anything for static pressure (DAMHIKT).
To your question on CFM for a refrigerator compressor it looks like they're in the 1 CFM (28 liter/minute) range and capable of ~100 PSI. Surprising number of examples of "homemade air compressors" on Youtube using these pumps. They are oil piston compressors just like typical large compressors so I suppose it does make sense.
Isn't the flow keeping the ping-pong balls aloft, not the pressure? I have seen in vacuum cleaner shops where they have a beach ball hovering above their latest model cleaner. I would think it would not require very much pressure at all, but a decent flow rate.
What about a CPAP machine? One would think that it's capabilities would mimic those of a human's, due to the way they function.